Skill: Find common factors

A common factor is a positive whole number that divides two or more numbers with no remainder.

To find common factors:

1. List the factor pairs for each number.
2. Write all the factors in each number’s set.
3. Identify the numbers that appear in both sets.

Example: Find the common factors of $(18)$ and $(24)$.

First, find the factor pairs of $(18)$:

$$1 \times 18,\quad 2 \times 9,\quad 3 \times 6$$

So the factors of $(18)$ are:

$$\{1,2,3,6,9,18\}$$

Next, find the factor pairs of $(24)$:

$$1 \times 24,\quad 2 \times 12,\quad 3 \times 8,\quad 4 \times 6$$

So the factors of $(24)$ are:

$$\{1,2,3,4,6,8,12,24\}$$

Now identify the numbers that appear in both sets:

$$\{1,2,3,6\}$$

Therefore, the common factors of $(18)$ and $(24)$ are:

$$\boxed{1,2,3,\text{ and }6}$$

Check: each of these numbers divides both $(18)$ and $(24)$ evenly.